Risk/Reward Ratios

I need away to compare one trade over another to determine whether its parameters made the trade better or not. Ideally, a one trade would be better than the next if its

  • Risk was reduced
  • Reward was increased
  • Number of trades were greater than equal
  • Trade duration was decreased
  • Win Ratio was increased (but not at the cost of higher drawdowns)

Reward is straightforward and we will generally use either the Expected Return as a percentage, or the profit in dollars on a trade of 10 contracts (I use 10 contracts for all trade simulations).

Risk can be measured several different ways. A common way to measure risk is the Value at Risk (VaR) or the maximum amount one could loose in the trade. With hedged credit positions, this would effectively be the

     VaR = Cash Margin Required – Net Premium Recieved.

For hedged debit positions, it would simply be the cash paid to acquire the position.

A more conservative measure would use the entire Margin for ROI since with most brokers that cash is unavailable for any other use.

We can also measure risk on a broader scale by looking at the Maximum Drawdown (MaxDD) which is measured as the largest drop from peak to trough for a portfolio or series of trades. We could measure it as the maximum value of summation of contiguous losses in our simulation. I like the MaxDD as another indicator as it helps inform you of how big an impact a trade may have on your portfolio. MaxDD for me is helpful in determining how much I am willing to allocate to any one trade. I am much more comfortable allocating a little more to a trade with a MaxDD of 20% than 80% even if the latter trade offers far more profit potential.

There are many different risk-to-reward metrics that can be used to compare trades. Probably the most common in the investing world is the Sharpe Ratio

     Sharpe = ExpRet / StdDev

I personally don’t like the Sharpe Ratio as it penalizes any significant upside returns.

A metric commonly used to compare hedge funds is the Sortino Ratio. This ratio uses the Downside Risk instead of the Standard Deviation so that no upside returns are penalized.

The Calmar ratio is a similar measurement that uses the MaxDD instead of SD, but also uses the CAGR. The Calmar is handy if you are compounding returns, and it is a more straightward calculation, but I am not interested in compounding for these tests.

While I like these metrics, they don’t really speak to the magnitude of the losses. For instance, one might have lots of medium losses, split by moderate gains.

The Profit Factor (PF) ratio takes into account the magnitude of gains and losses

     PF = SUM(Gains)



I like this measurement for its simplicity. Anything with a PF > 1 is profitable (the gains outweigh the losses). But as with all the previously described metrics, it does not tell us about either how frequently a trade wins, or number of trades a given scenario produces.

To solve the first issue, we also look at the Win Ratio:

     Win Ratio = # Winning Trades


# Loosing Trades

Comparing trades simply by their Win Ratio would be foolish, but the Win Ratio speaks to my personal comfort level. While I have heard some traders say they don’t care about their win ratio, but only that their average expected winning trade exceeds there average expected loosing trade (or PF > 1), I personally am more comfortable with trades that have a high win ratio and a high PF.

To solve the second issue, we need to also take into account the number of trades each scenario produces. Many scenarios may in fact have an infinite PF, but less than 1 trade per year. Is that a good scenario to bank on? Probably not. First, the number of trades is probably not statistically significant to ensure future performance; Second, there is a chance that you may have to wait a long time to find another trade again.

For this, I simply chart the Profit Factor against the Number of Trades for each scenario. I also eliminate any trades with less than 10 total trades (that’s ~1 trade per year) from my reports.

One other metric to highlight is the year-over-year returns. I don’t generally report these in this blog, but the yearly returns are available in my spreadsheets for each scenerio. It is interesting to tease out which scenarios performed well during the downturn in 2008 and 2011. We have to double-check the data to see whether any positive performance during this period was due to luck or due to scenario’s parameters.

My excel reports can actually return all these metrics (and more), but when evaluating different test runs, I need to focus on just a few that provide me the biggest bang for my buck.

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